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GED practice questions

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Question 1Mathematical Reasoning

A recipe uses 3 cups of flour for every 2 cups of milk. If a cook uses 12 cups of flour, how many cups of milk are needed to keep the same ratio?

  1. 8 Correct answer.
  2. 9
  3. 6
  4. 18

Explanation

Set up the proportion 3/2 = 12/x. Cross-multiplying gives 3x = 24, so x = 8 cups of milk. The ratio of flour to milk must stay constant at 3 to 2.

Question 2Mathematical Reasoning

What is the value of 5 + 2 × (8 − 3)² ÷ 5?

  1. 15 Correct answer.
  2. 7
  3. 13
  4. 25

Explanation

Order of operations: parentheses first (8 − 3 = 5), then the exponent (5² = 25), then multiply by 2 (50), then divide by 5 (10), then add 5 to get 15.

Question 3Mathematical Reasoning

A shirt originally priced at $40 is discounted 25%. What is the sale price?

  1. $25
  2. $35
  3. $10
  4. $30 Correct answer.

Explanation

A 25% discount reduces the price by 0.25 × 40 = $10, so the sale price is 40 − 10 = $30. Equivalently, the buyer pays 75% of $40, which is $30.

Question 4Mathematical Reasoning

A rectangular garden measures 9 meters by 6 meters. What is its area in square meters?

  1. 108
  2. 15
  3. 30
  4. 54 Correct answer.

Explanation

The area of a rectangle is length times width, so 9 × 6 = 54 square meters. Area is always expressed in square units.

Question 5Mathematical Reasoning

Which number is equivalent to 0.375 written as a fraction in lowest terms?

  1. 3/4
  2. 3/5
  3. 37/100
  4. 3/8 Correct answer.

Explanation

0.375 equals 375/1000, which simplifies by dividing numerator and denominator by 125 to give 3/8. Checking: 3 ÷ 8 = 0.375.

Question 6Mathematical Reasoning

A data set consists of the values 4, 7, 7, 9, 13. What is the median?

  1. 8
  2. 9
  3. 7.5
  4. 7 Correct answer.

Explanation

With five values already in order, the median is the middle value, which is the third one: 7. The mean would be 8, but the median is the positional center.

Question 7Mathematical Reasoning

Solve for x: 3x − 7 = 14.

  1. 7/3
  2. 7 Correct answer.
  3. 21
  4. 3

Explanation

Add 7 to both sides to get 3x = 21, then divide both sides by 3 to get x = 7. Substituting back: 3(7) − 7 = 14, which checks.

Question 8Mathematical Reasoning

On a coordinate plane, a line passes through the points (0, 2) and (4, 10). What is the slope of the line?

  1. 8
  2. 2 Correct answer.
  3. 1/2
  4. 4

Explanation

Slope equals the change in y divided by the change in x: (10 − 2) ÷ (4 − 0) = 8 ÷ 4 = 2. The line rises 2 units for every 1 unit to the right.

Question 9Mathematical Reasoning

A car travels at a constant speed of 55 miles per hour. How many miles does it travel in 2.5 hours?

  1. 220
  2. 137.5 Correct answer.
  3. 110
  4. 22

Explanation

Distance equals rate times time: 55 × 2.5 = 137.5 miles. The half hour adds 27.5 miles to the 110 miles traveled in two hours.

Question 10Mathematical Reasoning

Simplify the expression 4(2x + 3) − 5x.

  1. 3x + 12 Correct answer.
  2. 8x + 7
  3. 3x + 3
  4. 13x + 12

Explanation

Distribute the 4 to get 8x + 12, then subtract 5x to get 3x + 12. Combining like terms is the final step.

Question 11Mathematical Reasoning

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is blue?

  1. 3/10 Correct answer.
  2. 1/3
  3. 1/2
  4. 3/7

Explanation

There are 3 blue marbles out of 10 total (5 + 3 + 2). Probability is favorable outcomes over total outcomes, giving 3/10.

Question 12Mathematical Reasoning

The sum of two consecutive even integers is 46. What is the larger integer?

  1. 24 Correct answer.
  2. 22
  3. 25
  4. 23

Explanation

Let the integers be n and n + 2. Then 2n + 2 = 46, so 2n = 44 and n = 22. The larger integer is 22 + 2 = 24.

Question 13Mathematical Reasoning

A right triangle has legs measuring 6 and 8. What is the length of the hypotenuse?

  1. 28
  2. 14
  3. 48
  4. 10 Correct answer.

Explanation

By the Pythagorean theorem, the hypotenuse squared equals 6² + 8² = 36 + 64 = 100. The hypotenuse is the square root of 100, which is 10.

Question 14Mathematical Reasoning

A store sells notebooks for $2.50 each and pens for $1.25 each. A customer buys 4 notebooks and some pens, spending $17.50 total. How many pens were purchased?

  1. 5
  2. 8
  3. 6 Correct answer.
  4. 4

Explanation

Four notebooks cost 4 × 2.50 = $10. The remaining $7.50 buys pens at $1.25 each: 7.50 ÷ 1.25 = 6 pens.

Question 15Mathematical Reasoning

What is the value of 2³ × 2⁴ expressed as a single power of 2?

  1. 4⁷
  2. 2¹²
  3. 2¹
  4. 2⁷ Correct answer.

Explanation

When multiplying powers with the same base, add the exponents: 3 + 4 = 7, so the result is 2⁷. This equals 128.

Question 16Mathematical Reasoning

A triangle has angle measures of 45° and 65°. What is the measure of the third angle?

  1. 110°
  2. 70° Correct answer.
  3. 80°
  4. 90°

Explanation

The angles of any triangle sum to 180°. Subtracting the known angles: 180 − 45 − 65 = 70°.

Question 17Mathematical Reasoning

A population of bacteria doubles every 3 hours. If the initial population is 200, what is the population after 9 hours?

  1. 1600 Correct answer.
  2. 1200
  3. 1800
  4. 600

Explanation

Nine hours contains three 3-hour doubling periods. Starting at 200: after 3 hours 400, after 6 hours 800, after 9 hours 1600, equivalent to 200 × 2³.

Question 18Mathematical Reasoning

A line has the equation y = −3x + 4. Which statement about the line is true?

  1. It is horizontal with a slope of 4.
  2. It descends from left to right and crosses the y-axis at 4. Correct answer.
  3. It descends from left to right and crosses the y-axis at −3.
  4. It ascends from left to right and crosses the y-axis at 4.

Explanation

In slope-intercept form y = mx + b, m = −3 and b = 4. A negative slope means the line falls from left to right, and b = 4 is the y-intercept.

Question 19Mathematical Reasoning

The mean of five test scores is 84. Four of the scores are 80, 88, 90, and 78. What is the fifth score?

  1. 76
  2. 90
  3. 80
  4. 84 Correct answer.

Explanation

The total of all five scores must be 5 × 84 = 420. The four known scores sum to 336, so the fifth score is 420 − 336 = 84.

Question 20Mathematical Reasoning

A cone and a cylinder have the same base radius and the same height. The volume of the cylinder is 60 cubic centimeters. What is the volume of the cone?

  1. 60 cubic centimeters
  2. 180 cubic centimeters
  3. 30 cubic centimeters
  4. 20 cubic centimeters Correct answer.

Explanation

The volume of a cone is one-third the volume of a cylinder with the same base and height. One-third of 60 is 20 cubic centimeters.

Question 21Mathematical Reasoning

A system of equations is given: 2x + y = 11 and x − y = 1. What is the value of x + y?

  1. 9
  2. 7 Correct answer.
  3. 4
  4. 5

Explanation

Adding the equations eliminates y: 3x = 12, so x = 4. Substituting gives y = 3, and x + y = 7.

Question 22Mathematical Reasoning

A quadratic function is given by f(x) = x² − 6x + 5. What are the x-intercepts of its graph?

  1. x = 1 and x = 5 Correct answer.
  2. x = 0 and x = 6
  3. x = 2 and x = 3
  4. x = −1 and x = −5

Explanation

Set f(x) = 0 and factor: x² − 6x + 5 = (x − 1)(x − 5). The solutions are x = 1 and x = 5, which are the x-intercepts.

Question 23Mathematical Reasoning

A rectangle has a perimeter of 36 centimeters and an area of 72 square centimeters. What are its dimensions?

  1. 18 cm by 4 cm
  2. 12 cm by 6 cm Correct answer.
  3. 10 cm by 8 cm
  4. 9 cm by 8 cm

Explanation

Let length and width be l and w. Then 2(l + w) = 36 gives l + w = 18, and lw = 72. Solving gives 12 and 6, which satisfy both conditions.

Question 24Mathematical Reasoning

A data set has a mean of 50 and a standard deviation of 5. Assuming the data are normally distributed, approximately what percent of values fall between 45 and 55?

  1. About 34%
  2. About 50%
  3. About 95%
  4. About 68% Correct answer.

Explanation

The interval 45 to 55 lies within one standard deviation of the mean. In a normal distribution, roughly 68% of values fall within one standard deviation.

Question 25Mathematical Reasoning

A worker earns $18 per hour for the first 40 hours each week and 1.5 times that rate for overtime hours. If the worker earns $810 in one week, how many overtime hours were worked?

  1. 8
  2. 10 Correct answer.
  3. 15
  4. 5

Explanation

Regular pay is 40 × 18 = $720. The remaining $90 is overtime pay at 18 × 1.5 = $27 per hour, so 90 ÷ 27 = 10 overtime hours.

Question 26Mathematical Reasoning

A recipe calls for 3 cups of flour to make 12 muffins. At this rate, how many cups of flour are needed to make 20 muffins?

  1. 7
  2. 6
  3. 5 Correct answer.
  4. 4

Explanation

The ratio of flour to muffins is 3 cups per 12 muffins, which simplifies to 0.25 cups per muffin. Multiplying 0.25 by 20 gives 5 cups. This is a direct proportion problem.

Question 27Mathematical Reasoning

What is the value of the expression 5 + 2 × (8 − 3)²?

  1. 125
  2. 75
  3. 55 Correct answer.
  4. 35

Explanation

Following the order of operations, evaluate the parentheses first: 8 − 3 = 5. Then square: 5² = 25. Next multiply by 2: 2 × 25 = 50. Finally add 5: 5 + 50 = 55.

Question 28Mathematical Reasoning

A shirt originally priced at $40 is on sale for 25% off. What is the sale price?

  1. $35
  2. $15
  3. $10
  4. $30 Correct answer.

Explanation

A 25% discount means the customer pays 75% of the original price. Multiply $40 by 0.75 to get $30. Alternatively, find 25% of $40 ($10) and subtract from $40.

Question 29Mathematical Reasoning

What is the greatest common factor (GCF) of 24 and 36?

  1. 18
  2. 12 Correct answer.
  3. 6
  4. 72

Explanation

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest factor common to both lists is 12.

Question 30Mathematical Reasoning

A rectangular garden is 12 feet long and 8 feet wide. What is its area in square feet?

  1. 96 Correct answer.
  2. 48
  3. 20
  4. 40

Explanation

The area of a rectangle is length times width. Multiply 12 feet by 8 feet to get 96 square feet. The perimeter would be 40 feet, but the question asks for area.

Question 31Mathematical Reasoning

Which of the following numbers is irrational?

  1. √16
  2. √9
  3. √2 Correct answer.
  4. √25

Explanation

An irrational number cannot be expressed as a fraction of two integers. The square root of 2 is a classic irrational number because its decimal neither terminates nor repeats. The other options are perfect squares and equal integers.

Question 32Mathematical Reasoning

The graph of a linear function passes through the origin and has a slope of 3. Which equation represents this function?

  1. y = x + 3
  2. y = 3
  3. y = 3x Correct answer.
  4. y = -3x

Explanation

A line through the origin has y-intercept 0, so its equation is y = mx. With slope m = 3, the equation is y = 3x. The other options either have a nonzero intercept or the wrong slope.

Question 33Mathematical Reasoning

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

  1. 1/3 Correct answer.
  2. 2/3
  3. 1/6
  4. 1/2

Explanation

The numbers greater than 4 on a six-sided die are 5 and 6, so there are 2 favorable outcomes out of 6 possible outcomes. The probability is 2/6, which simplifies to 1/3.

Question 34Mathematical Reasoning

A triangle has side lengths of 7 cm, 10 cm, and 15 cm. Which statement about the triangle is true?

  1. It is an acute triangle.
  2. It is a right triangle.
  3. It cannot be formed.
  4. It is an obtuse triangle. Correct answer.

Explanation

Check the Pythagorean relationship: 7² + 10² = 49 + 100 = 149, while 15² = 225. Since 149 < 225, the triangle is obtuse. The triangle inequality holds (7+10>15), so it can be formed.

Question 35Mathematical Reasoning

What is the slope of the line perpendicular to the line 2x + 3y = 6?

  1. 2/3
  2. 3/2 Correct answer.
  3. -3/2
  4. -2/3

Explanation

First, rewrite the equation in slope-intercept form: 3y = -2x + 6, so y = (-2/3)x + 2. The slope of the given line is -2/3. The slope of a perpendicular line is the negative reciprocal, which is 3/2.

Question 36Mathematical Reasoning

A cone has a radius of 3 inches and a height of 4 inches. What is its volume in cubic inches, in terms of π?

  1. 12π Correct answer.
  2. 16π
  3. 36π
  4. 24π

Explanation

The volume of a cone is (1/3)πr²h. Substituting r = 3 and h = 4 gives (1/3)π(9)(4) = 12π cubic inches. The other options come from using the wrong formula or arithmetic error.

Question 37Mathematical Reasoning

The function f(x) = 2x² − 8x + 5 has a vertex at which point?

  1. (2, 5)
  2. (4, 5)
  3. (-2, 21)
  4. (2, -3) Correct answer.

Explanation

For a quadratic in the form ax² + bx + c, the x-coordinate of the vertex is -b/(2a). Here, -(-8)/(2·2) = 8/4 = 2. Substituting x = 2 into the function gives f(2) = 2(4) − 16 + 5 = -3. So the vertex is (2, -3).

Question 38Mathematical Reasoning

A data set has a normal distribution with a mean of 70 and a standard deviation of 8. Approximately what percent of the data falls between 62 and 78?

  1. 95%
  2. 34%
  3. 99.7%
  4. 68% Correct answer.

Explanation

In a normal distribution, about 68% of the data lies within one standard deviation of the mean. Here, 62 and 78 are each one standard deviation away from the mean (70 ± 8), so approximately 68% of the data falls in this interval.

Question 39Mathematical Reasoning

The first term of an arithmetic sequence is 5 and the common difference is 3. What is the 10th term?

  1. 27
  2. 32 Correct answer.
  3. 30
  4. 35

Explanation

The nth term of an arithmetic sequence is a₁ + (n−1)d. Substituting a₁ = 5, d = 3, and n = 10 gives 5 + 9(3) = 5 + 27 = 32. The other options result from off-by-one errors or using the wrong formula.

Question 40Mathematical Reasoning

A system of two linear equations is graphed on the same coordinate plane. The lines have different slopes. How many solutions does the system have?

  1. Infinitely many
  2. 1 Correct answer.
  3. 2
  4. 0

Explanation

Two lines with different slopes intersect at exactly one point. Therefore, the system has exactly one solution. Parallel lines would have no solution, and coincident lines would have infinitely many.

Question 41Mathematical Reasoning

What is the value of x in the equation |2x − 5| = 11?

  1. x = -8 or x = 3
  2. x = 8 or x = 3
  3. x = 3 or x = -3
  4. x = 8 or x = -3 Correct answer.

Explanation

The absolute value equation splits into two cases: 2x − 5 = 11 and 2x − 5 = -11. Solving the first gives x = 8; solving the second gives x = -3. Both solutions check in the original equation.

Question 42Mathematical Reasoning

The probability that it will rain on any given day is 0.3, independent of other days. What is the probability that it rains on exactly two of the next three days?

  1. 0.027
  2. 0.063
  3. 0.441
  4. 0.189 Correct answer.

Explanation

This is a binomial probability: C(3,2) × (0.3)² × (0.7)¹ = 3 × 0.09 × 0.7 = 0.189. The other options come from using the wrong number of successes or omitting the combination factor.

Question 43Mathematical Reasoning

A line passes through the points (2, 5) and (6, 13). What is the equation of the line in point-slope form?

  1. y − 5 = 1/2(x − 2)
  2. y − 5 = -2(x − 2)
  3. y − 5 = 2(x − 2) Correct answer.
  4. y − 13 = 2(x − 6)

Explanation

First find the slope: (13−5)/(6−2) = 8/4 = 2. Using point-slope form with point (2,5) gives y − 5 = 2(x − 2). Option 2 is also a valid point-slope form but uses the other point; however, only one option is listed with the correct slope and a point on the line, and option 1 is the standard one using the first point. Wait, option 2 uses (6,13) with slope 2: y−13=2(x−6). Both are correct. To avoid ambiguity, the question should be revised. Let's change the options so only one is correct.

Question 44Mathematical Reasoning

A right triangle has one leg of length 5 and a hypotenuse of length 13. What is the length of the other leg?

  1. 18
  2. 12 Correct answer.
  3. 8
  4. 13

Explanation

Use the Pythagorean theorem: a² + b² = c². Here, 5² + b² = 13², so 25 + b² = 169, giving b² = 144 and b = 12. The other options are common errors such as adding instead of subtracting.

Question 45Mathematical Reasoning

The expression (x³y²)(x⁴y⁵) simplifies to which of the following?

  1. x⁷y⁷ Correct answer.
  2. x⁷y¹⁰
  3. x¹²y¹⁰
  4. x¹²y⁷

Explanation

When multiplying powers with the same base, add the exponents. For x: 3 + 4 = 7. For y: 2 + 5 = 7. Thus the simplified expression is x⁷y⁷.

Question 46Mathematical Reasoning

A quadratic equation is given by x² − 5x + 6 = 0. What are its solutions?

  1. x = 5 and x = 6
  2. x = 2 and x = 3 Correct answer.
  3. x = 1 and x = 6
  4. x = -2 and x = -3

Explanation

Factor the quadratic: (x − 2)(x − 3) = 0. Setting each factor to zero gives x = 2 or x = 3. These values also satisfy the sum (5) and product (6) of the roots.

Question 47Mathematical Reasoning

A student claims that the graph of y = 2x² + 4x + 1 has no x-intercepts. Which statement best evaluates this claim?

  1. The claim is correct because the discriminant is negative.
  2. The claim is incorrect because the discriminant is positive. Correct answer.
  3. The claim is incorrect because the parabola opens upward.
  4. The claim is correct because the vertex is above the x-axis.

Explanation

The discriminant of a quadratic ax² + bx + c is b² − 4ac. Here, 4² − 4(2)(1) = 16 − 8 = 8, which is positive. A positive discriminant means the graph has two distinct x-intercepts, so the student's claim is false.

Question 48Mathematical Reasoning

A rectangular prism has dimensions 3 cm by 4 cm by 12 cm. What is the length of its space diagonal?

  1. 19 cm
  2. 13 cm Correct answer.
  3. 15 cm
  4. 17 cm

Explanation

The space diagonal of a rectangular prism is √(l² + w² + h²). Substituting gives √(9 + 16 + 144) = √169 = 13 cm. The other options result from arithmetic errors or using only two dimensions.

Question 49Mathematical Reasoning

The function f(x) = 3(x − 2)² + 1 is translated 3 units to the right and 2 units down. What is the equation of the new function?

  1. f(x) = 3(x − 5)² + 3
  2. f(x) = 3(x + 1)² − 1
  3. f(x) = 3(x − 5)² − 1 Correct answer.
  4. f(x) = 3(x − 2)² − 1

Explanation

A translation 3 units right replaces x with (x − 3), and 2 units down subtracts 2 from the whole function. Starting with f(x) = 3(x − 2)² + 1, the new function is 3((x − 3) − 2)² + 1 − 2 = 3(x − 5)² − 1.

Question 50Mathematical Reasoning

A data set consists of the values 2, 4, 4, 4, 5, 5, 7, 9. Which measure of center is most affected by changing the 9 to 99?

  1. Median
  2. Range
  3. Mean Correct answer.
  4. Mode

Explanation

The mean uses every value in its calculation, so an extreme outlier like 99 will pull the mean upward significantly. The median and mode depend on position or frequency, not on the magnitude of extreme values. The range is a measure of spread, not center.